Self-Organised Critical Dynamics as a Key to Fundamental Features of Complexity in Physical, Biological, and Social Networks

Abstract

Studies of many complex systems have revealed new collective behaviours that emerge through the mechanisms of self-organised critical fluctuations. Subject to the external and endogenous driving forces, these collective states with long-range spatial and temporal correlations often arise from the intrinsic dynamics with the threshold nonlinearity and geometry-conditioned interactions. The self-similarity of critical fluctuations enables us to describe the system using fewer parameters and universal functions that, on the other hand, can simplify the computational and information complexity. Currently, the cutting-edge research on self-organised critical systems across the scales strives to formulate a unifying mathematical framework, utilise the critical universal properties in information theory, and decipher the role of hidden geometry. As a prominent example, we study the field-driven spin dynamics on the hysteresis loop in a network with higher-order structures described by simplicial complexes, which provides a geometric-frustration environment. While providing motivational illustrations from physical, biological, and social systems, along with their networks, we also demonstrate how the self-organised criticality occurs at the interplay of the complex topology and driving mode. This study opens up new promising routes with powerful tools to address a long-standing challenge in the theory and applications of complexity science ingrained in the efficient analysis of self-organised critical states under the competing higher-order interactions embedded in complex geometries.